Question

Simplifique as expressões: a) (n + 4)!/(n + 2)! = (n + 3)! b) (n - 1)! + n!/ (n + 1)!

Answer 1

$a) \frac{(n+4)!}{(n+2)!}= \frac{(n+4)(n+3)(n+2)!}{(n+2)!} = (n+4)(n+3) = n^{2}+3n+4n + 12 \\ \\ n^{2}+ 7n + 12 \\ \\ b) \frac{(n-1)!+n!}{(n+1)!} = \frac{(n-1)!}{(n+1)!} + \frac{n!}{(n+1)!} = \frac{(n-1)!}{(n+1).n.(n-1)!} + \frac{n!}{(n+1).n!} \\ \\ \frac{1}{(n+1).n} + \frac{1}{(n+1)} = \frac{n+1}{(n+1).n} = \frac{1}{n}$

Espero ter ajudado.